To be honest, I actually think it'd be worse if Dick had offered Tim the Nightwing mantle. While if this was the case, Dick and Tim's fallout probably wouldn't have happened or at least not be as bad as it was, Bruce would still come back, Dick would want Nightwing back and guess what? Tim is fired, AGAIN.
I get what you’re saying but listen.
The reason things were so bad for Tim is because all he did was lose, lose, lose and either have people brush off his grief and anxiety/depression or outright ignore him. The period following Bruce’s death was the worst period in his life, probably one of the worst experiences of loss an grief any of the Bats have gone through since he lost basically his whole support system. The point of offering Nightwing wouldn’t have been about the costume, it would have been about the attention.
By offering Tim Dick’s old costume, he would be saying “Look I know things are hard for all of us right now but Damian needs Robin. But I still love you Tim and I trust you to wear my costume and honor the name.” Instead of letting Tim feel lost and abandoned and have him run off on a crazy ass quest; Dick should have held out an olive branch in the form of the Nightwing costume. I think it would have been nice, Tim falling into a well established costume, a safety net, to cope without struggling with the identity crisis that came from the Red Robin costume.
Not to mention, yes, when Bruce came back and Dick took the costume back, it had helped Tim mentally and emotionally in the short term. Instead of being kicked off a building and forced to recover on his own, he was given a chance to find himself within his grief and put himself back together. Had Dick been more available for Tim during that period, I believe he would have been happy to hand over the Nightwing costume and finally be ready to look for his own solo identity. Because it wasn’t so much losing the Robin costume itself that hurt, it was the betrayal of handing over the costume Tim had given up everything for to the 10 year old blood son who had done nothing (yet) to earn the title by the big brother he once thought had his back. That’s the part that stung.